"soar, glide on motionless wings," early 15c., from Old French planer "to hover (as a bird), to lie flat," from plan (n.) "plane," from Latin planum "flat surface" (see plane (n.1)), on notion of bird gliding with flattened wings. Of boats, etc., "to skim over the surface of water," it is first found 1913. Related: Planed; planing.

"tree of the genus Platanus," late 14c., from Old French plane, earlier plasne (14c.), from Latin platanus, from Greek platanos, earlier platanistos "plane tree," a species from Asia Minor, associated with platys "broad" (see plaice (n.)), in reference to its leaves. Applied since 1778 in Scotland and northern England to the sycamore, whose leaves somewhat resemble those of the true plane tree.

"to make smooth," early 14c., "to gloss over, explain away;" mid-14c. as "to make smooth or even," from Old French planer "to smooth, level off; wipe away, erase" (12c.), from Late Latin planare "make level," from Latin planus "level, flat" (see plane (n.1)). In early use in English often plain. Related: Planed; planing.